show all work b and c PTS 1 TOP: Decision Analysis 16. The Video Game Supply Com

Question

show all work b and c

PTS 1 TOP: Decision Analysis 16. The Video Game Supply Company (VGS) is dedding whether to set production next year at 2,000 2,500, or 3,000 games. Dem and could be low, medum, or igh. Using historical data, VGS estim ates the probabilities as 04 for low demand 0.3 for medum demand, and 0:3 for high demand The following profit payoff table in $100s) has been devetoped Quantity Demanded High 1400 Medium Production Target 2000 2,500 3,000 Low 1,000 800 600 1,500 1,700 1,400 a. Determine the expected value of each altemative andindcate what should be the production target b. Determine the expected value with pertect information about the st ates of nature. c. Determine the expected value of perfect infomation. ANS

Explanation / Answer

Solution

Back-up Theory

EMV (Expected Monetary Value) for a Decision Di = ?(pay-off under SONj) x (probability of SONj), summed over all possible j, where SON stands for State of Nature………. (1)

When the pay-off is profit, the optimal decision is that Di with the maximum EMV…..(2)

Expected Value Under Perfect Information (EVPI): Since perfect information on SON is available, there is no uncertainty. Hence, for each SON, the best decision is that Di for which the pay-off is maximum. EVPI = ?(bets pay-off under SONj) x (proportion of times for SONj), summed over all possible j ……………………………………………………(3)

Expected Value of Perfect Information = EVPI – Best EMV ……………………………(4)   

Part (a)

Pay-off Table and EMV Calculations: [vide (1) above]

Decision

(Production 103)

Pay-off - $106(given)

EMV

SON (Demand)

Low

Medium

High

D1: 2.0

1.0

1.2

1.4

1.18

D2: 2.5

0.8

1.5

1.3

1.16

D3: 3.0

0.6

1.7

1.4

1.17

P(SON)

0.4

0.3

0.3

Since 1.18 is the maximum EMV, [vide (2) above], the corresponding decision, D1, namely, produce 2000 is the optimal decision. ANSWER

Part (b)

Expected Value Under Perfect Information

Vide (3),

SON

Best Pay-off

Proportion of SON

Low

1.0 under D1

0.4

Medium

1.7 under D3

0.3

High

1.4 under D1

0.3

So, EVPI = (1.0 x 0.4) + (1.7 x 0.3) + (1.4 x 0.3) = 1.33 x 106 ANSWER

Part (c)

Expected Value of Perfect Information = 1.33 – 1.18

= 0.15 x 106 ANSWER

Decision

(Production 103)

Pay-off - $106(given)

EMV

SON (Demand)

Low

Medium

High

D1: 2.0

1.0

1.2

1.4

1.18

D2: 2.5

0.8

1.5

1.3

1.16

D3: 3.0

0.6

1.7

1.4

1.17

P(SON)

0.4

0.3

0.3

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.